We

1

• Well now consider 2x2 contingency tables, a
  table which has only 2 rows and 2 columns along
  with a special way to analyze it called Fishers
  Exact Test.
• See Table 5.5.1 on page 173 X the number of
  observations in row 1, column 1 out of n10.
  Since there are 7 obs. in row 1, and 3 in row 2,
  under the null hypothesis of no association
  between the row and column variables, all
  10choose7 possibilities of arrangements of 7 in
  row 1 and 3 in row 2 are equally likely. Thus we
  may compute the null distribution of X as shown
  on p.173-174. For an upper-tailed test, we
  compute the probability of being gt the value we
  found in our table and this becomes the p-value
  for Fishers exact test. Go over Example 5.5.1
  on p.174 do with SAS also note this is a
  lower-tailed test so we compute the probability
  that X lt 3 to get the p-value.
• In SAS, if the table is 2x2, then Fishers exact
  test is automatically computed
• data table5_5_2
• input drug pe count _at__at_ datalines
• 1 1 3 1 2 8 2 1 4 2 2 4
• proc freq tables drugpe exact chisq
• weight count run quit
• In R, Fishers exact test is computed with
• fisher.test

2

• If you have paired data with dichotomous
  responses, then McNemars test is appropriate.
  The example given in Table 5.8.1 is a good one
  to assess whether a debate changes a voters
  mind, we find out who a voter favors before and
  after the debate (paired). Table 5.8.1 shows the
  results... The hypothesis being tested is that
  the probability of switching from A to B is the
  same as the probability of switching from B to A.
  Let XAB the number of switches from A to B and
  XBA the number of switches from B to A. Under
  the null hypothesis of equal chance of switching
  from A to B as B to A, XAB is just like the sign
  test statistic with a B(n, .5) distribution.
  Standardize it and use Z or square the
  standardized statistic and use chi-square with 1
  degree of freedom this implementation is
  typically called McNemars test.
• Apply this to the data in Table 5.8.1 SAS
  implements McNemars test in PROC FREQ. R has
  mcnemar.test
• HW Read sections 5.5 (Fishers Exact Test) and
  5.8 (McNemars Test). Do 7-9,12 and 13 at the
  end of Ch. 5. Begin reading in Chapter 8,
  Bootstrap Methods...